Duplicating surface of cube adds a circle to it
This is because when you duplicate the face, it is now a flat plane and the subdivision surface modifier is treating it as a separate mesh and rounding it.



To get around this, you can disable or hide the modifier while working by clicking the eye icon  on the Subsurf modifier.

If I also understand what you are trying to do, it's also worth noting that you don't need to duplicate the face to apply a material to it or to modify it specifically. Objects can have multiple materials in Blender. You can go to the material tab, select a specific face, add a new material and apply it specifically to that face by clicking Assign.